The Progressive-X\(^+\)  algorithm is motivated by two observations about the nature of multi-model fitting problems.
First, even though all state-of-the-art algorithms [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} formalize the problem as a clustering where a set of data points (cluster) represents a model instance, this assumption is incorrect in a number of real-world scenes.
Moreover, one of the primary reasons of multi-model fitting algorithms often being fairly slow stems from the optimization techniques, \(\alpha \) -expansion in PEARL [1]}, needed to solve the point-to-model assignment problem.
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